Filter banks (FBs) play an important role in a number of digital signal processing (DSP) applications. They are usually employed in two basic configurations: First, a broadband signal is decomposed into its narrowband components, with the so called Analysis Filter Bank (AFB), for further processing and then the broadband signal is reconstructed back with the help of the Synthesis Filter Bank (SFB). In the second configuration, many narrowband signals are combined into one broadband signal with the SFB and then are reconstructed again with the AFB. The first configuration is usually called Sub-band Coding (SBC) and involves applications like, for example, signal compression, adaptive sub-band processing, channel equalization and spectrum sensing. The second configuration is the so called transmultiplexer (TMUX) and it is mainly applied to wired and wireless communications systems, where a number of data streams of one or more users are combined into one broadband signal to be transmitted via some medium and in the receiver, the different streams are then recovered. Modulated Filter Banks (MFB) are between the most popular FB classes because they have implementation structures with very low computational complexity.
The most prominent use of MFBs is in multicarrier modulation schemes. Those schemes are frequently called Filter Bank based Multicarrier (FBMC). The most trivial FBMC system is the so called Orthogonal Frequency Division Multiplexing (OFDM). OFDM utilizes a trivial prototype filter (all ones) and does not achieve maximum spectral efficiency due to the cyclic prefix. OFDM has been used in different wired and wireless standards, like ADSL, VDSL, WiFi and LTE, the 4th Generation of cellular systems. In the discussions of future mobile communications standards, more specifically the 5th Generation (5G), more general implementations of FBMC systems are under consideration. One of the candidate schemes is FBMC with the symbols in each subcarrier using Offset Quadrature Amplitude Modulation (OQAM) mapping.